Consider the set of positive integers N+ = {1, 2, 3, .....}. Let LN denote a set of integer lists. Members?

Question

Members of LN are as follows. < 1, 1 >, < 2, 2, 1, 1 >, < 3, 3, 2, 2, 1, 1>, < 4, 4, 3, 3, 2, 2, 1, 1> ... and so on.Give inductive definition of set LN. You may use cons, head, tail etc operations on a list.

Answer 1

Using + to denote list concatenation (and also addition, which meaning is intended should be clear from context):

L_1 = <1, 1>
L_(n+1) = + L_n

LN = {L_n: n∈N}

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